Question: Vanessa is 4 times as old as William and is also 21 years older than William. How old is Vanessa?
We can use the given information to write down two equations that describe the ages of Vanessa and William. Let Vanessa's current age be $v$ and William's current age be $w$ $v = 4w$ $v = w + 21$ Now we have two independent equations, and we can solve for our two unknowns. One way to solve for $v$ is to solve the second equation for $w$ and substitute that value into the first equation. Solving our second equation for $w$ , we get: $w = v - 21$ . Substituting this into our first equation, we get the equation: $v = 4$ $(v - 21)$ which combines the information about $v$ from both of our original equations. Simplifying the right side of this equation, we get: $v = 4v - 84$ Solving for $v$ , we get: $3 v = 84$ $v = 28$.